Season chicken breasts with salt and pepper on both sides.
Heat olive oil in Instant Pot on Sauté mode and brown chicken in batches, 3-4 minutes per side until golden. Remove to a plate.
Add butter and garlic to pot and cook 30 seconds until fragrant.
Stir in tomato paste and cook 30 seconds, then add flour and stir to combine.
Deglaze with white wine, scraping up browned bits as wine reduces by half.
Add thyme, chili flakes, sun-dried tomatoes, and chicken stock. Stir well.
Return chicken to pot and close lid. Pressure cook on high for 2 minutes.
Allow 5 minutes natural release, then manually release remaining pressure.
Remove chicken with slotted spoon and set aside.
Set Instant Pot to Sauté and add cream. Simmer 3-4 minutes until sauce thickens slightly.
Stir in basil ribbons.
Return chicken to sauce to heat through and serve over rice, pasta, or mashed potatoes.